Stabe rank of graph algebras: Type I graph algebras and their limits

Abstract

For an arbitrary countable directed graph E we show that the only possible values of the stable rank of the associated Cuntz-Krieger algebra C* (E) are 1, 2 or ∞. Explicit criteria for each of these three cases are given. We characterize graph algebras of type I, and graph algebras which are inductive limits of C*-algebras of type I. We also show that a gauge-invariant ideal of a graph algebra is itself isomorphic to a graph algebra.